Deep Learning Methods Of Mathematical Physics - Volume I: Direct And Inverse Problems

This book explores how Artificial Intelligence and Deep Learning are transforming Mathematical Physics, offering modern data-driven tools where traditional analytical and numerical methods fall short. As physical systems grow more complex or chaotic, deep learning provides efficient surrogates and physics-informed models capable of capturing dynamics and uncovering governing laws directly from data. This book introduces Neural ODEs, Physics-Informed Neural Networks (PINNs), and Hamiltonian and Lagrangian Neural Networks, showing how they enhance classical mechanics and PDE solvers for both forward and inverse problems. With Keras code examples, Google Colab notebooks, and practical exercises, this book serves researchers and students in physics, mathematics, and engineering seeking a concise, hands-on guide to applying deep learning in physical systems.

Ovidiu Calin is a distinguished professor at Eastern Michigan University and has served as a visiting professor at Princeton University and the University of Notre Dame. He has been awarded a Fulbright Fellowship in Artificial Intelligence and has delivered lectures in Canada, Japan, Hong Kong, Taiwan, Kuwait, the UK, and Romania. He earned his PhD from the University of Toronto in the field of geometric analysis.

Dr Calin is the author or co-author of several notable books and monographs, including Computational Formalisms in Euclidean Geometry,/i> (World Scientific, 2025), Stochastic Geometric Analysis with Application (World Scientific, 2023), Stochastic Calculus with Applications (World Scientific 2015, 2021), Deep Learning Architectures (Springer 2020), Deterministic and Stochastic Topics in Computational Finance (World Scientific 2016), Geometric Modeling in Probability and Statistics (Springer, 2014), Heat Kernels for Elliptic and Sub-elliptic Operator (Birkhäuser, 2010), Sub-Riemannian Geometry (Cambridge Press, 2009), Geometric Analysis on the Heisenberg Group and Its Generalizations (AMS/IP, 2007), and Geometric Mechanics on Riemannian Manifolds (Birkhäuser, 2004).